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Myra ran $4$ laps on Tuesday, $9$ laps on Wednesday, $16$ laps on Thursday, and $25$ laps on Friday. What kind of sequence is this? $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Identify arithmetic and geometric sequences

Full solution

Q. Myra ran

4

laps on Tuesday,

9

laps on Wednesday,

16

laps on Thursday, and

25

laps on Friday. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

(C) both

\newline

(D) neither

Identify Sequence: Identify the sequence of the number of laps Myra ran each day. $\newline$ Tuesday: $4$ laps $\newline$ Wednesday: $9$ laps $\newline$ Thursday: $16$ laps $\newline$ Friday: $25$ laps $\newline$ Sequence: $4, 9, 16, 25$
Check Arithmetic: Check if the sequence is arithmetic by finding the differences between consecutive terms. $\newline$ $9 - 4 = 5$ $\newline$ $16 - 9 = 7$ $\newline$ $25 - 16 = 9$ $\newline$ The differences are not constant, so the sequence is not arithmetic.
Check Geometric: Check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ $\frac{9}{4} \approx 2.25$ $\newline$ $\frac{16}{9} \approx 1.78$ $\newline$ $\frac{25}{16} \approx 1.56$ $\newline$ The ratios are not constant, so the sequence is not geometric.
Determine Sequence Type: Since the sequence has neither a constant difference nor a constant ratio, determine the type of sequence. $\newline$ The sequence is neither arithmetic nor geometric.

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